LOS ANGELES, Nov. 20 (Ticker) -- Kobe Bryant was at times unstoppable but rarely was unselfish.

Bryant scored a league season-high 43 points but took seemingly every shot for the Los Angeles Lakers, missing his final four attempts in a 96-93 loss to the Chicago Bulls, who posted their first road win of the season.

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A seven-time All-Star, Bryant made 17-of-34 shots as he hoisted at least 25 for the ninth time in 10 games this season and at least 30 for the fourth time.

"I really don't want to shoot the ball that many times," Bryant said. "It's important for other people to step up and make contributions. With me, taking 30-something shots is the key to our success. With that being said, and the flow of the game, if baskets need to be made, I have to step up and keep us competitive."

"When a guy scores 43 points, it's hard to say you did a pretty good job on him," Bulls coach Scott Skiles said. "He's as difficult a matchup as there is in the league. But overall, we have to be pleased with the effort we put on him. He is a great player."

Bryant poured in 37 points through the first three quarters but failed to take over down the stretch, shooting just 2-of-7 in the final period. Even worse, he left his teammates without the confidence or offensive rhythm necessary to pick up his slack.

With about eight minutes remaining, Bryant emerged in transition and split two defenders with a beautiful wraparound move, making a layup for a three-point play. He added a 20-foot jumper on the next possession for an 84-77 lead with 7:20 left but did not score again.

"When Bryant gets hot like that, what do you do, really, - just hope he misses," said Bulls guard Kirk Hinrich, who scored 16 points and dished out eight assists. "When he makes jump shots like that, how do you cover the guy? We just tried to stay with it, challenge all his jump shots aggressively."

"We did a great job, we had an eight-point lead," Bryant said. "We didn't lose the game because of our offense. But defensively, we just had too many mental breakdowns. We gave them wide open looks at the basket. We can't do that down the stretch."

The Bulls, who came in with a three-game losing streak, ended the contest on an 11-1 run while showing that two scoring options are better than one. Chris Duhon and Hinrich combined for 19 of Chicago's 22 fourth-quarter points, with each drilling huge 3-pointers down the stretch.

"We have struggled out here (on the West Coast)," Hinrich said. "But we're happy to go back home with a win. We got one."

Lakers guard Smush Parker sank a shot from the arc for a 92-85 lead with 4:03 left, but Hinrich and Duhon answered with consecutive 3-pointers to bring Chicago within a point.

Andres Nocioni completed the comeback with a driving layup to give the Bulls a 93-92 lead with 1:59 remaining, but Lamar Odom answered with a free throw to tie it with 1:25 to go.

After the teams exchanged empty possessions, Chicago's Mike Sweetney drove to the rim and was clobbered by Lakers rookie center Andrew Bynum. Sweetney, who finished with 20 points and 12 rebounds, made 1-of-2 from the line to give the Bulls a 94-93 lead.

The Lakers opted not to take a timeout, instead pushing the ball upcourt. Bryant forced a shot, attempting an off-balance jumper over three defenders that failed to hit the rim.

"Their defense collapsed over and I got hit on the arm way up," Bryant claimed. "On those situations, you never get the call, anyway."

Duhon sank a pair of free throws to push the lead to three points. On the Lakers' final possession, Bryant's 3-pointer clanged off the front rim and Odom's game-tying attempt at the buzzer rimmed off.

"I had a shot, missed it. Lamar had a shot, missed it. Game over," Bryant said.

A 2004 second-round pick, Duhon continued to prove himself to be an overachiever, pouring in 11 of his 21 points in the fourth quarter. The former Duke star made 5-of-7 shots from the arc, adding eight assists and five rebounds.

"Chris got hot and everything kind of went from there," Hinrich said.

Other than Bryant, Chris Mihm was the only Laker in double figures, scoring 13 quiet points. Parker was the only other Laker to take more than seven shots, making 3-of-12 for eight points.

"That's the way it's been the last couple of nights," said Lakers forward Brian Cook, who had seven points off the bench. "I know something has got to change, not with (Bryant), because we want him to score. But something is going to have to change. We're going to have to play D and believe in each other. If we believe in each other, anything can happen."